Layered composite materials have been used in many applications in engineering products from a patio to an airplane. When building an aircraft, for example, engineers need lightweight, strong material that can insulate and protect passengers while surfacing the aircraft. An aircraft made of pure metal could fail catastrophically if a small crack appeared in the skin of the airplane. On the other hand, aircraft integrating reinforced composite materials such as fiberglass, graphite, and other hybrids will be stronger and less likely to break up. Layered composite materials comprise an arbitrary number of layers or plies as shown in FIG. 1.
Finite element analysis (FEA) is a computer implemented method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional, non-linear structural design, and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells, and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material identifier to associate with its material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
Using FEA to numerically simulate structural behaviors of layered composite materials contained in a structure can be done with existing technologies (i.e., FEA application module executed in a computer system). However, there is a problem for prior art approaches. In particular, this problem occurs when a large number of different composite materials are used in a structure (e.g., modern aircraft) or when the number of layers and their material properties change continuously throughout a given structural component. The user (e.g., engineers and/or scientists) prefer to reference the given structural component with one identifier in the FEA model, but they are required to identify elements that have identical number of layers and material properties associated with the layers and give them a unique identifier. Thus, a given component is broken up into multiple parts with each part made up of disjoint element groups with one or more elements per group. For example, the prior art approach is tedious, manual and/or semi-manual ad-hoc and often confusing for the user. Not only is the prior art approach time-consuming, it is also error-prone and requires additional effort when the computation output is analyzed.
A related problem associated with the prior art approach is that efficient computer processing techniques such as vectorization and domain decomposition in massive parallel processing cannot be applied optimally when parts use layered composite materials that vary continuously in the number of layers and material properties. For this to occur, the elements of each unique part identifier must be processed together, which implies that the number of layers and material properties must be the same and the elements are stored in contiguous memory locations. However, these shell finite elements are often scattered in the FEA model. Efficient massive parallel processing requires load balancing across all processors. In composite shell finite elements, the time required to process each shell element is proportion to the number of layers which can lead to unbalanced processor loads depending upon the element distribution in the FEA model.
Therefore, it would be desirable to have an improved method for obtaining numerically simulated structural behaviors of layered composite materials contained in a structure in a time-marching simulation using finite element analysis.